I'm writing this in response to this list. When I had found it, I hoped to see a long list of new books that I didn't know of. Instead, I found only seven books and it horribly lacking in some of the classics I grew up with as a child. I had recommended horse books to a friend already and she suggested that I make up a list, so here you go! Most of this is based off of my own reading habits and opinions, some of which are many years old. I will also warn that I am horrible at judging what age people should be reading each book, so I'll try and warn as best as I can about anything that might be triggery.
I'll say sorry right now for how long it is. We'll start off with the series of my 'childhood'. Please note that the dates I'm putting with these are the original publication dates. Most of them have been reprinted, so don't use those dates for searches.
The Black Stallion series by Walter Farley (1941-1989)
21 books (25 if you count the 4 that Steven Farley wrote) in total that follow the adventures of Alec Ramsay and the black stallion who he was shipwrecked on an island with, the stories of the Black's offspring, the adventures of Steve Duncan and the fiery red stallion he finds on a secret island, and two stand alone stories (one about Henry's horse tamer brother and a fictionalized biography of Man O' War). I devoured these during elementary school. I loved the movies and loved the books even more.
While the stories focus on horse racing, there are many different types of books within the series, including a bit of the supernatural, mysteries, and even aliens. While the world has changed a great deal since Walter Farley wrote these books, I had no problem loving them. I also haven't read them in a long time or as an adult, so I'm not sure if there are any snafus I might have missed while I was a kid. There are sad parts (character deaths, etc) as well as plenty of action, violence, and horrible people, but from my memories, nothing so bad that it would be traumatizing. This could also just be the nature of the Black Stallion. It does deal with stallions as most of the main horse characters after all and, being based off the Bucephalus myth, none of them are really the odd sweet, docile stallions that pop up every now and then.
Also, depending on what versions of the books you can get, you might also be met by wonderful ink illustrations within the pages.
A continuation of these is the four Steven Farley books (2000-201) that I mentioned above. While it has the same characters, there is something missing between his interpretation and his father's.
For another alternative, there is the Young Black Stallion series (6 books - 1998-1999) by Steven Farley. It follows the story of Danielle who must deal with her family selling their farm to Alec Ramsay and her beloved horse. Luckily, she has Raven, the Black's new colt, to keep her busy, even if he proves to be quite the handful. I've only read the first of this series and while it was enjoyable, it wasn't the same as the original series to me.
For younger reader books, Walter Farley also put out three easy readers: Little Black, a Pony, Little Black Goes to the Circus and The Little Black Pony Races as well as a picture book version of The Black Stallion called Big Black Horse. I'm not sure how available any of these are though.
If anyone wants specifics on any of the books, feel free to ask.
Marguerite Henry's Books (1945-1996)
She's written a good deal of books and I haven't read all of them, but what I have is wonderful. She is the woman who made Chincoteague famous. Most of her books are fictional historical in one way or another and beautifully illustrated by Wesley Dennis. I have fond memories of these books as through elementary school, my mom and I would sit down every night and would read them together. Because these vary more than the Walter Farley books, I'll run down the list. Like with the Black Stallion books, I haven't read these in a long time, so there may be things that I've missed.
Misty of Chincoteague (1947) - Most likely her most famous book following the story of Paul and Maureen and the Pony Penning festivities on Chincoteague. Wonderful family atmosphere. Plenty of problems both action based and more mundane to solve.
Stormy, Misty's Foal (1963) - A sequel to Misty. While it is about the horses, it is mainly about the Ash Wednesday Storm that devasted the islands in 1962 and the aftermath of trying to rebuild after it. I'll admit, I had to look up the plot as I couldn't remember it very well from the last time we read it.
Sea Star, Orphan of Chincoteague (1949) - Another sequel to Misty. When the Beebe family sells Misty to cover bills, Paul and Maureen are left with a hole in their life. When they find an orphaned foal, they focus on helping the foal survive. Again, I had to look up the plot to this one as even though I was sure I had read it, I couldn't fully remember the plot.
Justin Morgan Had a Horse (1945) - a fictional biography of the foundation stallion of the Morgan horse breed. Very fun and very much a 'the little horse that could' story.
King of the Wind (1948) - The fictional biography of one of the foundation stallions for the Thoroughbred breed. Much in the same vein as Justin Morgan Had a Horse, but it is laden with more depressing problems as Sham, a Godolphin Arabian, is born not only with a sign that he'll be bad luck, but a sign too that he'll be fast. The book follows the horse and his groom's unlucky journey from Morocco to England and eventually a happy ending.
Born to Trot (1950) - I had to look up the plot to make sure I had actually read this. It is a book focused on harness racing and Gibson and Rosalind's journey to the Hambletonian (one of the biggest horse races in harness racing). I want to say that there is some racing violence (sulkies overturning/being dragged), but I can't remember if that's this book or The Black Stallion's Blood Bay Colt.
Album of Horses (1951) - This is a BEAUTIFUL book. It is filled with wonderful, full page color illustrations as well as ink doodles in the sides of the pages. It is more of a reference book than a story, going into a few horse breeds and their histories/uses.
Brighty of the Grand Canyon (1953) - I have this book, but I think I've only really looked through the illustrations and never read it. It follows the story of a little burro that lives in the Grand Canyon. I know there's a bit of violence (there's a cougar attack somewhere in there and recuperating from that), but I don't think it's anything too horrible.
Black Gold (1957) - I will warn you right up front that this book has a sad ending. I remember BAWLING over the last few chapters. It's the fictional biography of an American Thoroughbred racehorse named Black Gold, so if you want an idea of what the book will be about, you can read his wiki page. It was a good book, but the end is heartbreaking.
Mustang, Wild Spirit of the West (1966) - This is another one that might be better for older kids. I read it in middle school and it deals with the treatment of the mustangs and Annie Johnston's campaign to get them protection. The main graphic part is the description of how the mustangs are rounded up. I remember reading it and being horrified by it and then getting angry when everyone patronized Annie's quest to stop that from happening. Another part of the book is Annie dealing with having polio (which I didn't remember) and that the characters get a bit religious (another thing I didn't remember).
San Domingo, the Medicine Hat Stallion (1972) - If I remember correctly, this deals with the pony express as well as Native American rights. I remember there being a few sad parts, but nothing too bad.
Here are the rest of the horse books she wrote that I haven't read:
Gaudenzia, Pride of the Palio
White Stallion of Lipizza
One Man's Horse
Our First Pony
Brown Sunshine of Sawdust Valley
The Saddle Club series by Bonnie Bryant (1986-2001)
101 books as well as super editions and inside stories following the adventures of best friends Lisa, Carole, and Stevie at Pine Hollow Stable. I had these books for awhile, but I don't think I started reading them until middle school/high school as just fun 'quick' reads. It's a good series, much in the way of the Babysitter's Club and such. It deals with horses and a child can learn a great deal about a lot of different disciplines (jumping, dressage, western, racing, etc) from the book. It also deals with many pre-teen/teen issues from boys to jealousy to anorexia to loss of a loved one. There are hard moments in the series (in the second book there is a character death), but it deals with it realistically. When I read them, I have to say I was jealous of all the cool things that happened at their stable and the friendships the three girls had. I can't remember what the last book I read was, but I know that I haven't read all 101.
For alternative to this, there are also the spin-offs: Pony Tails (16 books) for younger readers and Pine Hollow (17 books) for older readers. From what I know Pony Tails follows the adventures of younger students at Pine Hollow. Pine Hollow is a continuation of Saddle Club in that it's Lisa, Carole, and Stevie in high school. I haven't read any of the Pony Tails books, but I read the first of Pine Hollow. I didn't read more as its focus is much more on the teen drama/people than on the stable and the horses, but it is definitely more of a teen book as it deals mainly with a car crash and the repercussions of the crash.
Thoroughbred series by Joanna Campbell (1991-2005)
This was a series that I was reading at the same time I was reading the Saddle Club. Started by Joanna Campbell, there are 72 books in this series (plus 4 super editions). I've only read to around the 20s, so I can't say much about the later plot lines and the quality of writing. The series starts out with Ashleigh moving to Townsend Acres and saving the life of a small filly named Wonder. For a time, the series follows Ashleigh and Wonder's journey through the racing world before it branches off to focus on other characters and Wonder's children. Part way through the series, there's a time jump and it focuses more on eventing, but eventually makes it back to horse racing. I enjoyed the start of the series, especially with it focusing on women in the racing world. It has its sad moments like the Saddle Club, but it generally handles them well. I think the sad parts are also just a given in a way because of how dangerous horse riding and especially horse racing can be.
There's a 'continuation' of the series in the Ashleigh series (15 books) that follows Ashleigh's life before he moved to Townsend Acres. I haven't read this one, but considering the circumstances that lead Ashleigh to move (a deadly virus wipes out her family's farm), I can't imagine the series ends on a happy note.
The Silver Stallion series by Elyne Mitchell (1958-2003)
I had gotten interest in this series from the movie, the Silver Stallion (with a young Russell Crowe), early on, but didn't get to read them until I was in college and was actually able to purchase a good deal of her books when I visited Australia. I'm not sure how available they are due to that.
There are 16 'brumby' books in the series. The main storyline follows the story of Thowra, a rare creamie brumby, in the Snowy Mountains of Australia. It follows his life of trying to survive and form his own herd without being killed by rival stallions or captured by the man on the black horse. The later books follow his offspring and their own trials, travels, and tribulations. In the same vein, she also has a series of books about brumbies that don't feature Thowra or his children. I've read most of the Silver Stallion books and her writing is beautiful. I however have no idea what age level these books are for. There is some horse violence and some character death, but it isn't anything particularly gruesome.
Edit: Another added:
The Serendipity books
For a younger readership and I know there are mixed feelings about these books in regards to their messages/story telling. The pictures are gorgeous though and I remember them better than the actual words. I suppose it shows how much of an artist I am in that as a child I would constantly pick these up and look at them, but I don't think I ever read them more than one time through. It was always about the pictures to me.
As far as I know, here are the horse/unicorn/pegasus specific ones:
Unicorn: Misty Morgan
Morgan and Me
Morgan and Yew
Horse: Mumkin - a personal favorite with the cute little pudgy ponies!
I'll leave this entry's listing to that! I'll post something later about more individual horse books that are out there. Of course, I know there are plenty other series out there, these are just the ones that I know the best. Also, if anyone wants individual book listings on any of these, feel free to ask and I'll add them into the comments.